39-EFT.WP.Plasma.Confinement v1.0 | Chapter 13 — Experimental Design & Falsification (M20-*)

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Chapter 13 — Experimental Design & Falsification (M20-*)

I. Chapter Objectives & Structure

1. Objective: Build Plasma Confinement positive/negative criteria and power analysis, define reproducible protocols, controls, and release gates so S20-/S30-/S40-/S50-/S60-/S70-/S80-/I10-/M10- close under a unified metrology/recording dialect and are falsifiable.
2. Structure: Test matrix & controls → Criteria & sample size → Observation geometry & experiment design → Data cleaning & blinding → Reference experiments & workflow → Failure modes & troubleshooting → Compliance templates → Cross-chapter closure.
3. Shared arrival-time dialect (two equivalent forms; explicit gamma(ell) & d ell; record delta_form):
   • Constant-factored: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • General: T_arr = ( ∫ ( n_eff / c_ref ) d ell )

II. Test Matrix & Controls (Overview)

1. Primary endpoints:
   • Power closure: P_in = P_ref + P_rad + P_wall + ∫ P_dep dV (S50-/S80-).
   • Topology consistency: q(ψ), LCFS/X/separatrix consistent with imaging/magnetics (S30-/I10-).
   • Stability gates: δW_min > 0, Δ' ≤ 0, {D_S,D_M}>0 (S40-).
   • Deposition consistency: P_dep(r) peak/width vs {n_eff,k_∥,k_⊥} predictions (S50-).
   • Transport scaling: D,χ vs D_GB/tabulated closures (S70-).
   • Arrival consistency: two-dialect T_arr within u(T_arr) (S50-/M10-).
2. Controls:
   • Negative controls: off-resonance/zero injection/reference geometry & currents.
   • Positive controls: known stable/unstable configurations; calibrated ECH/NBI modulation.

III. M20-PC-1 Criteria & Sample Size (Criteria & Power)

• P1 Power-closure criterion:
• | P_in − P_ref − P_rad − P_wall − ∫ P_dep dV | ≤ u_power → positive

failure → negative.

• P2 Topology consistency: maximum deviation between magnetics/MSE-inverted q(ψ) and GS q(ψ) satisfies max_ψ |Δq| ≤ q_gate.
• P3 Stability-energy criterion: δW_min > 0 and Δ' ≤ 0; any failure → negative.
• P4 Deposition consistency: peak(P_dep) offset ≤ r_gate vs {n_eff,k_∥,k_⊥} prediction; width ≤ w_gate.
• P5 Transport-scaling criterion: linear regression of log(D/χ) vs log(D_GB)/target scalings has R^2 ≥ R^2_gate and residual ≤ ε_gate.
• P6 Arrival-time criterion:
• | T_arr^{(n_over_c)} − T_arr^{(one_over_c_times_n)} | ≤ u(T_arr)
• Power analysis (mean/slope difference exemplar):
• N ≥ 2 · (( z_{1−α/2} + z_{1−β} ) · σ / |δ| )^2

Suggested: engineering 1−β ≥ 0.8, α ≤ 0.05; release 1−β ≥ 0.9, α ≤ 0.01.

IV. Observation Geometry & Experiment Design (execution dialect)

• Equilibrium & coils: from I10-/S30- provide psi_bc, I_coil, LCFS/X; for small perturbation scans, record ΔI/I and X-point drift.
• Waves/heating: configure ECH/ICRF/LH frequency, polarization, launch angles; provide {n_eff,k_∥,k_⊥} and ray/full-wave settings; record coherence window & Δt_sync.
• Guiding-center/transport: choose observation surfaces, ensure consistency of V'(ψ) and metrics; annotate section values of ρ_*,β,ν_*.
• Wall & targets: target angle, B_t/B_p, material and γ_q for q_t acceptance and detachment gates.
• Records: arrival{form,gamma,measure,c_ref,Tarr,u_Tarr,delta_form}, qa_gates, spectral windows/bandwidths/sampling.

V. Data Cleaning & Blinding

• Pre-registration: freeze frequency grid/window width, fitting method, gate thresholds, baseline_id, Znorm/T_mm/Z0_mm, binding_ref, delta_form.
• Blinding: shuffle/hide injection levels, geometry configs, and feedback labels; unblind after analysis.
• Cleaning flow: de-embed → renorm → S↔Z → sync correction → path/arrival → power closure → topology/stability → deposition/transport regression.
• Hard QA: check_dim=pass, power closure, topology consistency, two-dialect T_arr agreement.

VI. Reference Experiments & Workflow (reproducible)
A. ECH deposition scan (validates P1/P4/P6)

• Pre-register frequency/launch-angle/sweep windows;
• Acquire T_b(ω), arg Z(ω), P_dep(r) (inversion/tomography);
• Test power closure, P_dep peak/width, and two-dialect T_arr.

B. Magnetic topology scan (validates P2/P3)

• Small I_coil scans with GS regression;
• Compare q(ψ) inversion (magnetics/MSE) vs GS;
• Compute δW_min, Δ' and decide stability gates.

C. NBI modulation & transport regression (validates P1/P5)

• Square/triangular NBI modulation;
• Invert χ,D from thermal/density responses; regress vs scalings & D_GB;
• Power closure and residual gates.

D. Reflectometry arrival (validates P6)

• Record φ(ω), T_group(ω) and correct Δt_sync;
• Compare two T_arr dialects;
• Check consistency with S50- {n_eff,k_∥,k_⊥}.

VII. Failure Modes & Troubleshooting

• Power non-closure: calibration or deposition inversion errors in P_in/P_ref/P_rad/P_wall → re-check calibration & transfer operators.
• Topology mismatch: coordinate/grid inconsistency or psi_bc anchoring error → unify I10-/S30- grids & metrics.
• Stability conflict: δW/Δ' contradict spectral features → roll back boundary term/inner-layer model.
• Deposition misalignment: n_eff mode choice or optical geometry error → revise medium approximation/rebuild geometry.
• Transport residuals high: closure table out-of-bounds or S_k does not support QL assumptions → band-limit/update closure or use nonlinear model.
• Out-of-window arrival: phase fitting outside coherence window → restrict to Ω or use energy composition.

VIII. Compliance Templates (copy-ready)

• Experiment protocol card (YAML)
• protocol_pc:
• prereg:
• baseline_id: "BLSN-PC-001"
• binding_ref: "GEOM-COIL-0001"
• Znorm_ohm: [50.0, 50.0]
• Tmm_Z0mm: {T_mm:"/cfg/T_mm.yaml", Z0_mm_ohm:[100,25]}
• delta_form: "n_over_c"
• criteria: ["P1","P2","P3","P4","P5","P6"]
• alpha: 0.05
• power: 0.8
• configs:
• - {id:"ECH_scan", freq_GHz:[..., ...], angle_deg:[...]}
• - {id:"coil_sweep", dI_over_I:[...]}
• - {id:"NBI_mod", pattern:"square", duty:0.5}
• windows:
• freq_GHz: [f1, f2]
• coh_window: {ω1: ω1, ω2: ω2}
• acquisition:
• fs_Hz: 1.0e6
• repeats: 5
• sync:
• dt_sync_s: 1.0e-08
• arrival:
• form: "n_over_c"
• gamma: "explicit"
• measure: "d_ell"
• c_ref: 299792458.0
• qa_gates: ["check_dim","power_closure","topology_consistency","Tarr_dual"]
• Analysis skeleton (pseudocode)
• # De-embed/renorm → S↔Z
• Z = map_S_to_Z(renorm(deembed(S_raw, fixture), Znorm(ω)), Znorm(ω), T_mm=Tmm, Z0_mm=Z0mm)
• assert min(Re(Z)) >= 0.0 and KK_consistency(Z)
• # Arrival & phase
• phi = unwrap(arg(Z) - ω*Δt_sync)
• Tarr1 = (1/c_ref) * trapz(n_eff(ω)*dℓ) # n_over_c
• Tarr2 = trapz((n_eff(ω)/c_ref)*dℓ) # one_over_c_times_n
• assert abs(Tarr1 - Tarr2) <= u_Tarr
• # Power closure & deposition
• Pdep = integrate(P_dep_grid)
• assert abs(P_in - P_ref - P_rad - P_wall - Pdep) <= u_power
• # Topology & stability
• q_inv = invert_q_from_mse_mags(data)
• assert max_abs(q_inv - q_GS) <= q_gate
• assert deltaW_min > 0 and DeltaPrime <= 0
• # Transport regression
• Dfit, Chifit = regress_transport(fluxes, gradients, metrics)
• assert R2(Dfit, D_GB) >= R2_gate and resid(Dfit) <= eps_gate
• # Emit QA

IX. Cross-Chapter Links & Closure

• Dependencies: Chapters 2 (Terms & Symbols), 4 (S20- minimal equations), 5 (S30- equilibrium & topology), 6 (S40- stability & energy principle), 7 (S50- waves/deposition/arrival), 8 (S60- guiding center & neoclassical), 9 (S70- transport closures), 10 (S80- edge/wall), 11 (I10- implementation), 12 (M10- metrology & assimilation).
• Downstream: Chapter 14 (SimStack & benchmarks—make these criteria part of regression baselines), Chapter 15 (Data & Repro—equivalence & audit), Chapter 16 (Design Protocol & Checklist—integrate criteria & power into sign-off).